Use Green's Theorem And/or a Computer Algebra System to Evaluate $\int _ { C } x ^ { 2 } y d x - x y ^ { 2 } d y$

question 19

Multiple Choice

Use Green's Theorem and/or a computer algebra system to evaluate $\int _ { C } x ^ { 2 } y d x - x y ^ { 2 } d y$ , where $C$ is the circle $x ^ { 2 } + y ^ { 2 } = 64$ with counterclockwise orientation.

• A) \(8 \pi\)
• B) \(64 \pi\)
• C) \(2 \pi\)
• D) \(- 32 \pi\)
• E) None of these

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Definitions:

Observable Behaviour

Any action or reaction of a person or animal that can be directly observed and measured, excluding internal states or thoughts.

Conscious Experience

The awareness of one’s own thoughts, feelings, and sensations, allowing individuals to be cognizant of their environment and themselves.

Wundt

Refers to Wilhelm Wundt, often considered the father of experimental psychology, who established the first psychology laboratory.

Structuralism

An approach in psychology that analyzes the mind's structure by understanding the simplest definable components and then how they fit together in complex forms.